Theorems · Theorem · field theory

IsAlgebraic.of_ringHom_of_comp_eq

∀ {R : Type u} {S : Type u_1} {A : Type v} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Ring A]
  [inst_3 : Algebra R A] {B : Type u_2} [inst_4 : Ring B] [inst_5 : Algebra S B] {FRS : Type u_3} {FAB : Type u_4}
  [inst_6 : FunLike FRS R S] [inst_7 : RingHomClass FRS R S] [inst_8 : FunLike FAB A B] [inst_9 : RingHomClass FAB A B]
  (f : FRS) (g : FAB) {a : A},
  IsAlgebraic S (g a) →
    Function.Surjective ⇑f →
      Function.Injective ⇑g → (algebraMap S B).comp ↑f = (↑g).comp (algebraMap R A) → IsAlgebraic R a

Defined in

Mathlib.RingTheory.Algebraic.Basic

Cited by

4 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingRingAlgebraRingAlgebraFunLikeRingHomClassFunLikeRingHomClass